Psychiatrists have a very difficult time explaining why people crossdress or undergo sex changes. The urge to do so mostly appears to coincide with puberty, but many male children start putting on their mother's and sister's clothes and makeup at a much younger age.
The technical word for this phenomenon is transvestism and it's not to be confused with homosexuality since the two things are apparently unconnected. Most men that practice cross-dressing are transvestites and they appear quite normal when dressed in men's clothes, and the majority only have sex with women, and don't even dream of having their penises removed.
A transsexual is very different however, and he doesn't indentify with his body at all and he believes that nature made a mistake and that he's a woman trapped in a man's body. He'll often hate his penis and want to get rid of it and all costs, and will long for enlarged breasts.
The chances that a transvestite will later become a transsexual is highly unlikely and would be similar to somebody that's a social drinker becoming an alcoholic.